What is expand (-36-sqrt(x))^4 ?

The solution to expand (-36-sqrt(x))^4 is 1679616+186624sqrt(x)+7776x+144xsqrt(x)+x^2

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expand (-36-sqrt(x))^4

expand

(- 36 - x)^{4}

1679616 + 186624 x + 7776 x + 144 x x + x^{2}

Solution steps

(- 36 - x)^{4}

Apply binomial theorem:

(a + b)^{n} = i = 0 \sum n (i n) a^{(n - i)} b^{i}

a = - 36, b = - x

= i = 0 \sum 4 (i 4) (- 36)^{(4 - i)} (- x)^{i}

Expand summation

= \frac{4 !}{0 ! ( 4 - 0 ) !} (- 36)^{4} (- x)^{0} + \frac{4 !}{1 ! ( 4 - 1 ) !} (- 36)^{3} (- x)^{1} + \frac{4 !}{2 ! ( 4 - 2 ) !} (- 36)^{2} (- x)^{2} + \frac{4 !}{3 ! ( 4 - 3 ) !} (- 36)^{1} (- x)^{3} + \frac{4 !}{4 ! ( 4 - 4 ) !} (- 36)^{0} (- x)^{4}

Simplify

\frac{4 !}{0 ! ( 4 - 0 ) !} (- 36)^{4} (- x)^{0} : 1679616

Simplify

\frac{4 !}{1 ! ( 4 - 1 ) !} (- 36)^{3} (- x)^{1} : 186624 x

Simplify

\frac{4 !}{2 ! ( 4 - 2 ) !} (- 36)^{2} (- x)^{2} : 7776 x

Simplify

\frac{4 !}{3 ! ( 4 - 3 ) !} (- 36)^{1} (- x)^{3} : 144 (x)^{3}

Simplify

\frac{4 !}{4 ! ( 4 - 4 ) !} (- 36)^{0} (- x)^{4} : x^{2}

= 1679616 + 186624 x + 7776 x + 144 (x)^{3} + x^{2}

Simplify

(x)^{3} : x x

= 1679616 + 186624 x + 7776 x + 144 x x + x^{2}

(x - x) (x + 3 y) (4 y - 7 z) (4 + 3 x)

\frac{6 ( - 2 + x ^{\frac{4}{3}} ) ( 6 + x ^{\frac{4}{3}} )}{x ^{\frac{5}{3}}}

(- 36 - x)^{2}

(8 + π)^{2}

5 x^{2} + x y + (5 - 2) y^{2}

What is expand (-36-sqrt(x))^4 ?
The solution to expand (-36-sqrt(x))^4 is 1679616+186624sqrt(x)+7776x+144xsqrt(x)+x^2